A few comments are in order.
The weights of the matching graph edges in alg:decoder are derived from the homodyne measurement outcomes, as well as the positions of the \(p\) -squeezed states in the lattice.
An example of such weights is presented in Sec:Threshold.
Furthermore, using the homodyne measurement outcomes to calculate matching graph weights has been explored in the context of the toric code [1]}, [2]}, but the knowledge of the locations of the \(p\) -squeezed states gives us additional information that can be used to improve the performance of the decoder.
We discuss this point in more detail in Sec:Threshold.
